Quantifying Quantum Order Transitions in Cuprate High-Tc Superconductor

Wall turbulence and cuprates HTSC are similar for they are both complex systems with many degrees of freedom, and in non-equilibrium state with strong fluctuations. Here, we identify a new similarity between the two: both display symmetry-breaking transition embedded in nontrivial transport. First, we present a recent structural ensemble dynamics (SED) theory of wall turbulence that yields unified and accurate description of mean velocity and turbulent intensities profiles across the entire domain of turbulent boundary layer, using a multi-layer formula of a length order function quantifying turbulent eddy size (She et al., JFM, 2017,2018). Then, we extend the SED theory to cuprates HTSC to predict a similar length order function, which successfully describes transitions between several dominant quantum orders such as spin order, charge order and superconductivity, as validated by resistivity data (see also another contributed talk, Li and She, 'New mechanism of umklapp scattering in cuprate HTSC' ). We conclude that wall turbulence and cuprates HTSC share similar self-organized symmetry-breaking feature, which can be effectively described through length order function.